Functional Impulses in Exact Stochastic Simulation

Jumps which are observed in many population models give rise to fluctuations in the dynamics of systems. Deterministic model which is based on the Impulsive Differential Equations (IDEs) considers these jumps as impulses and defines the dynamics of the system between successive jump times with the Ordinary Differential Equations (ODEs). From our previous studies, we have proposed a model which is the complement of IDEs in the sense that both studies consider the jumps as impulses. The main difference between these two approaches is that the former implements ODEs to model the dynamics of system between successive jump times while the latter applies the Chemical Master Equation (CME). From the analyses we have shown that such impulses can be added to the system under the two main scenarios, namely, impulses at fixed time and impulses at fixed states. Hereby as the novelty in this work, we extend our model in such a way that if the jump function and the realization of the model intersect, we update the time to the intersection time point and update the state vector according to the jump function. We insert this idea in the exact Gillespie algorithm and assess the performance of our extended model in different epidemic modellings.
Citation Formats
D. Altıntan, V. Purutçuoğlu Gazi, and Ö. Uğur, “Functional Impulses in Exact Stochastic Simulation,” presented at the International Conference on Pure and Applied Mathematics (ICPAM 2015), (5 - 28 August 2015), Van, Türkiye, 2015, Accessed: 00, 2021. [Online]. Available: